Question

\(\left(x-7\right)^4+\left(x-8\right)^4=\left(15-2x\right)^4\)

Answer 1

Đặt \(\left\{{}\begin{matrix}x+7=a\\x-8=b\end{matrix}\right.\) phương trình trở thành:

\(a^4+b^4=\left(a+b\right)^4\)

\(\Leftrightarrow a^4+b^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4\)

\(\Leftrightarrow2ab\left(2a^2+3ab+2b^2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a=0\\b=0\\2a^2+3ab+b^2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}a=0\\b=0\\\left\{{}\begin{matrix}a=0\\b=0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}a=0\\b=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x+7=0\\x-8=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-7\\x=8\end{matrix}\right.\)